A high-throughput technique for determining grain boundary character non-destructively in microstructures with through-thickness grains

Abstract

Grain boundaries (GBs) govern many properties of polycrystalline materials. However, because of their structural variability, our knowledge of GB constitutive relations is still very limited. We present a novel method to characterise the complete crystallography of individual GBs non-destructively, with high-throughput, and using commercially available tools. This method combines electron diffraction, optical reflectance and numerical image analysis to determine all five crystallographic parameters of numerous GBs in samples with through-thickness grains. We demonstrate the technique by measuring the crystallographic character of about 1,000 individual GBs in aluminum in a single run. Our method enables cost- and time-effective assembly of crystallography-property databases for thousands of individual GBs. Such databases are essential for identifying GB constitutive relations and for predicting GB-related behaviours of polycrystalline solids.

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ARTICLE OPEN

A high-throughput technique for determining grain boundary character non-destructively in microstructures with through-thickness grains

Matteo Seita1, Marco Volpi2, Srikanth Patala3, Ian McCue4, Christopher A Schuh1, Maria Vittoria Diamanti2, Jonah Erlebacher4 and Michael J Demkowicz5

Grain boundaries (GBs) govern many properties of polycrystalline materials. However, because of their structural variability, our knowledge of GB constitutive relations is still very limited. We present a novel method to characterise the complete crystallography of individual GBs non-destructively, with high-throughput, and using commercially available tools. This method combines electron diffraction, optical reectance and numerical image analysis to determine all ve crystallographic parameters of numerous GBs in samples with through-thickness grains. We demonstrate the technique by measuring the crystallographic character of about 1,000 individual GBs in aluminum in a single run. Our method enables cost- and time-effective assembly of crystallographyproperty databases for thousands of individual GBs. Such databases are essential for identifying GB constitutive relations and for predicting

GB-related behaviours of polycrystalline solids.

npj Computational Materials (2016) 2, 16016; doi:http://dx.doi.org/10.1038/npjcompumats.2016.16

Web End =10.1038/npjcompumats.2016.16 ; published online 24 June 2016

INTRODUCTIONPolycrystalline materials are aggregates of differently oriented crystal grains joined along grain boundaries (GBs). Although they typically comprise a small fraction of the materials volume, GBs have tremendous impact on its properties, including strength and ductility,13 thermal and electrical conductivity,4,5 diffusion,6,7 resistance to environment-assisted failure,8,9 and radiation

tolerance.10,11 Although all grains may have identical crystal structure, GB structure depends at minimum on ve crystal-lographic parameters:12,13 three to describe the relative

misorientation, R, of the adjoining grains and two for the GB

normal vector, ^

n.

A growing body of evidence shows that many GB properties, , also depend on all ve of these parameters.1421 Thus, we may write GB constitutive relations as F R; ^

n

. Knowing these

relations is key to predicting the behaviour of polycrystals and to designing materials with superior properties.22 However, these relations are difcult to obtain experimentally because it is challenging to measure the property of interest, , and the full characteri.e., both R and ^

nof numerous individual GBs.

Measurement of GB properties, such as corrosion susceptibility, fracture strength or permeability, requires a physical test of the samples, which often irreversibly damages the GB or alters its character. Some techniques for determining GB character (GBC) involve the destruction of the sample, making it impossible to measure GB properties afterwards.

We have developed a new high-throughput method to measure GBC without altering the samples and thus allowing further testing to assess properties of individual GBs. Our method relies on the preparation of microstructures with through-thickness

grains and integrates measurements of R through electron backscatter diffraction (EBSD)23 with determinations of ^

n using

optical reectance microscopy (ORM):24 a hybrid technique we term EDOR (electron diffraction optical reectance). We demonstrate and validate EDOR on GBs in polycrystalline aluminum (Al). EDOR may be employed to collect the large experimental data sets needed to establish GB constitutive relations, F R; ^

n

.

Although the misorientation of GBs on free surfaces is easy to measure non-destructively using EBSD,23 nding GB plane normal vectors is usually harder.25 One approach to obtain them couples EBSD with focused ion-beam serial sectioning.26Although this is a versatile technique that may be employed on a wide range of microstructures and sample geometries, it requires the physical destruction of the GBs to measure their character, which prevents any further test aimed at measuring their physical properties. GBC may be found using transmission electron microscopy20 or three-

dimensional X-ray diffraction (3DXRD)2729 while leaving GBs available, in principle, for subsequent property measurements. However, transmission electron microscopy has limited throughputit can only study a few GBs at a timewhereas 3DXRD is cost- and time-intensiveit requires advanced X-ray sources and signicant computational effort to reconstruct GBC.30 The

advantage of EDOR over these techniques is its ability to assess GBC non-destructively, with high-throughput, and using commercially available equipment and software.

RESULTSFigure 1 illustrates the elements of EDOR. The method is intended for samples with through-thickness grains. Many commonly

1Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA; 2Department of Chemistry, Materials and Chemical Engineering G Natta, Politecnico di Milano, Milan, Italy; 3Department of Materials Science and Engineering, North Carolina State University, Raleigh, NC, USA; 4Department of Materials Science and Engineering, Johns Hopkins University, Baltimore, MD, USA and 5Materials Science and Engineering, Texas A&M University, College Station, TX, USA. Correspondence: M Seita (mailto:[email protected]

Web End [email protected])

Received 9 December 2015; revised 18 May 2016; accepted 20 May 2016

Published in partnership with the Shanghai Institute of Ceramics of the Chinese Academy of Sciences

High-throughput technique to determine GBC M Seita et al

2

encountered types of samples have such microstructures, including lms that have been epitaxially grown and then lifted off of their substrates31 or polycrystals that have been mechanically thinned into foils with thickness smaller than the average grain size.8 Not all such samples are representative of bulk micro-structures. However, our work is not aimed at investigating bulk microstructure, but rather at relating the crystallographic character of numerous individual GBs to their physical properties. Samples with through-thickness grains provide rich data sets to study these relationships, provided that the GBs within them sample a broad range of GBCs. Here we illustrate EDOR using engineered Al foils with through-thickness grains created by repeated rolling and annealing (see the Methods section). The foils are ~ 600-m thick and contain grains with average diameter of

~ 700 m. EDOR consists of (1) the non-destructive characterisation of the GB plane normal vectors ^

n using ORM, (2) assessment of the GB misorientation using EBSD and (3) integration of these two data sets into a list of complete GBCs for all GBs in the sample.

In the rst step, the GB plane normal vector ^

n in the laboratory frame is measured by analysing both sides of the sample through ORMa process illustrated in Figure 2. To reveal the crystal-lographic facets of the constituent grains, both sides of the sample are mechanically polished and then chemically etched (see the Methods section). A sequence of micrographs is acquired from both sides of the engineered sample under variable incident light direction using a stereographic optical microscope, as shown in Figure 2a. The reectance of a grain along a specic direction depends on the orientation of the crystallographic facets on its surface with respect to the incoming light.24 Thus, different grains appear with different intensity through the optical microscope as a function of both their crystallographic orientation and the direction of the incident light (Figure 2a). Each optical micrograph is then digitally segmented using a MATLAB processing routine (described in detail in Supplementary Information) that nds the GB traces on the sample surfaces using a contrast-based edge detection algorithm,32 as illustrated in Figure 2b. The algorithm identies GB traces by detecting discontinuities in intensity that are larger than a pre-specied threshold. This image processing routine detects all GBs in the microstructure, where a GB is dened by a crystallographic misorientation of 5, as in other techniques.23

Not all GBs appear in each optical micrograph. Acquiring multiple optical micrographs under different illumination conditions ensures that all GBs are detected in at least one of them. The digitalised micrographs are then summed into two cumulative TOP and BOTTOM micrographs that contain all detected GB traces from both sample sides, shown in Figure 2c. To remove noise arising from surface scratches or irregularities,

Figure 1. EDOR process to assess GB crystallography (top schematics) using through-thickness-grained microstructures. Left: optical reectance micrographs taken from the top and bottom of the sample are used to evaluate the GB plane normal vector. Right: EBSD characterisation on the top side of the sample is used to measure GB misorientation.

Figure 2. Evaluating GB plane normal vectors. (a) Acquisition of a sequence of optical micrographs under different illumination conditions. (b) Post-processing of each optical micrograph to detect GB traces using a contrast-based edge detection algorithm. (c) Reconstruction of the GB trace network from the top (blue) and bottom (red) of the sample by summing the sequence of processed optical micrographs. (d) Registration of the cumulative TOP and BOTTOM images to display the projected GB network (overlapping signal between TOP and BOTTOM displayed in purple). For interpretation of colours, the reader is referred to the web version of this article.

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High-throughput technique to determine GBC M Seita et al

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nx and ny are measured from the linear t to the top GB trace. We adopt the convention that the normal vector, ^

n, points from the

bottom side to the top.

To test the accuracy of this calculation, we permeate our Al sample with liquid gallium (Ga; Supplementary Information). Permeation of Ga into Al is intergranular and leads to the disaggregation of the microstructure into constituent grains without altering the grain shapes.33 We conrm the GB plane tilts calculated using EDOR by imaging individual grains using optical microscopy. Three illustrative grains are shown in Figure 3b. The measurement error, , in the computed GB plane tilt may arise from neglecting possible out-of-plane curvature of the boundary plane, from uncertainties in the evaluation of the GB trace distance, d, and from local variations in sample thickness, t, that result from non-uniform grinding during sample preparation. We inspect selected grain facets by scanning electron microscopy and nd that the out-of-plane curvature is negligible over the length of the GB (see Supplementary Figure S14 in the Supplementary Information). Following equation (1), we have

computed an error of

p

d2t

2 3 using conventional

uncertainty propagation techniques (Supplementary Information).

In the second step of EDOR, we nd GB misorientations. The top side of the sample is prepared for EBSD characterisation (see the Methods section). The EBSD data set is imported into MATLAB through MTEX,34 a toolbox used to compute misorientation angles and axes ^

o of each GB from the crystallographic orientation of the adjoining grains. In principle, EBSD or other electron-based microscopy techniques, such as orientation contrast imaging,35

may also be conducted on both sides of the sample and then used to reconstruct the GB networksimilar to how ORM operates in EDORor else performed on one side of the sample only and then combined with Monte Carlo simulations to infer the likeliest GB plane normal vector.36 These approaches are advantageous in that they all use scanning electron microscopy and do not require registration of different data sets. However, they are mostly suitable for small-size samples and become impractical for large samples due to EBSDs and orientation contrast imagings limited eld of view, slow scanning speed and large image distortion.37

For these reasons, EDOR relies on optical- rather than electron-based techniques to assess GB plane normal vectors.

Finally, in the third step of EDOR, the EBSD data ( and ^

o as well

as the orientations of the two adjacent grains, OA and OB) are automatically assigned to the corresponding GB plane normal vector ^

n, such that for each GB both the misorientation and plane normal vector are specied. This procedure is detailed in the Supplementary Information. The grain orientations obtained with EBSD are used to rotate the GB plane normal vector ^

n from the lab frame into the frames of the individual grains: ^

nA and ^

nB:

^

nA O-1AU^

n

t2d2d2t

2

Figure 3. Calculation and validation of GB plane tilt angle . (a) Evaluation of the distance d between top- and bottom-GB traces. The 3D schematic shows the orientation of the GB plane in the laboratory reference frame. (b) Comparison of grain shapes obtained through EDOR with direct images of the same grains after disaggregation of the Al microstructure via Ga permeation. The GB crossed in black is the only instance where the EDOR prediction does not match the actual plane tilt.

all features that have low cumulative signal are ltered out. This way, all GB traces from both top and bottom sides of the sample are found, with the exception of those that appear with low frequency in the cumulative images (Supplementary Information). TOP and BOTTOM are then registered in MATLAB using prefabricated ducial markers: through-thickness notches engraved by electric discharge machining around the perimeter of the sample (Supplementary Information). Registration may be performed manually by selecting control points at the notch vertices or automatically using a built-in MATLAB function that uses an intensity-based registration algorithm. The result is a single micrograph, shown in Figure 2d, that contains GB traces from both top and bottom sides of the engineered sample.

To evaluate the normal vector ^

n, we follow the procedure illustrated in Figure 3a. The tilt angle of the GB plane with respect to the top surface is computed from the sample thickness t at the GB location and the average distance d between the GB traces on the top and bottom sides:

arctan

d t

nB O-1BU^

^

n 3

^

: 1

t is estimated by interpolating the thickness values measured around the perimeter of the samples using a caliper, whereas d is computed automatically from the registered micrograph shown in Figure 2d (Supplementary Information). The GB plane normal vector ^

n (in the lab frame) may then be written as:

n

nx

n2

x

nA and ^

nB are representations of the same GB plane, expressed with respect to reference frames xed to the two adjoining crystal grains. In this paper, we use both ^

nA and ^

nB for representing each measured GB plane. We note that a unique representation of the GBCconsidering both misorientation and boundary planecan be found after considering all symmetry operations that stem from the underlying crystals.38 The implications of using such a representation on the formulation of GB constitutive relations will be discussed in a future publication.

DISCUSSIONUsing EDOR, we found the complete GBC of 976 GBs from three Al samples with cumulative area of ~ 1.4 cm2. Figure 4 presents the disorientationsusing the axis-angle parameterisation(Figure 4a) and boundary plane orientations (Figure 4b) of these GBs,

j j^z

h i

2

ny

n2

x

^ p cos

^x

n2 y

p cos

^y sin

n2 y

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Figure 4. Visualisation of the GBC distribution as measured by EDOR in polycrystalline Al. (a) GB misorientation distribution. The plot shows progressive slices of constant through the asymmetric fundamental zone for misorientations in cubic crystals. Each section comprises GBs within the specied range of 2.5 (indicated in degrees below each slice).43 (b) Distribution of the GB plane normal vectors plotted in the standard stereographic triangle for cubic symmetry.

showing an approximately uniform and diverse sampling of GBC. The misorientation distribution function of one representative Al sample is also reported in the Supplementary Information. All three Al samples remained undamaged by these measurements and were therefore available for subsequent measurements of GB properties. These results demonstrate that EDOR is a reliable, high-throughput and non-destructive technique to assess the GBC of numerous individual GBs in polycrystalline materials. It therefore provides a critical capability for nding GB crystallography property relationships, F R; ^

n

. Owing to its hybrid nature

which combines ORM and EBSDEDOR has higher versatility than other optical techniques and may therefore be applied to a wider range of materials.39 As it relies on commercially available equipment and software, EDOR may be widely adopted by many groups to study GB crystallographyproperty relations. The MATLAB scripts for EDOR as well as the raw data presented in this paper are provided in the Supplementary Information. As a proof of concept, we employed EDOR on Al samples created by repeated rolling and annealing. However, EDOR may also be employed on other types of samples, with grain size resolvable by ORM and sample thickness smaller than the average grain size. Modied versions of EDOR may be employed to characterise nanostructured materials or thin lms by means of transmission electron microscopy,40,41 or as an in situ characterisation tool in

layer-by-layer additive manufacturing.42 Further improvements to EDOR will aim at retrieving GB misorientations using ORM and at meshing the surface of curved GBs to extract variable GB plane normals.27 These upgrades will signicantly improve the efciency of EDOR at sampling the GB crystallography space, by removing the need for EBSDthe most time-intensive step in EDORand maximising the number of detected GBs per sample.

MATERIALS AND METHODSAl samples with through-thickness grains were produced from a 500-g high-purity Al (99.999%) master ingot. A ~ 20-mm-thick foil was cut from the master ingot and underwent a series of rolling and annealing cycles until the foil was ~ 600-m thick. Each cycle consisted of a 50% thickness reduction, chemical etching in 1 mol/l NaOH solution at 80 C for 15 min, and annealing at 620 C for 20 min. The amount of thickness reduction was tailored to ensure complete recrystallisation upon annealing, while limiting texture formation and minimising work hardening. The chemical etching was used to remove the native oxide lm that may form at each cycle and contaminate the rollers. The annealing temperature was chosen near the melting temperature of Al to maximise the kinetics of grain growth. Both sides of the Al samples with through-thickness grains were then mechanically polished using a sequence of SiC paper from 2,400 to 4,000 grit size. Subsequently, the samples were immersed in a bath of 1 N NaOH for 30 min in stirring condition to reveal the crystallographic facets of the

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Supplementary Information accompanies the paper on the npj Computational Materials website (http://www.nature.com/npjcompumats)

constituent grains. After having characterised the microstructure by optical reectance, one side of the sample (referred to as the top side) was further polished using a colloidal silica suspension (0.04 m) to a mirror-like quality and then characterised by EBSD.

ACKNOWLEDGEMENTS

We acknowledge O.K. Johnson for providing help with the MATLAB code and for stimulating discussions. This work was supported by the US Department of Energy, Ofce of Basic Energy Sciences under award no DE-SC0008926. M.V. was supported by the MISTI Seed Fund Progetto Roberto Rocca. I.M. and J.E. were supported by the National Science Foundation under grant DMR-1003901. Access to shared experimental facilities was provided by the MIT Center for Materials Science Engineering.

CONTRIBUTIONS

The project was planned and supervised by M.S., M.J.D., M.V.D. and C.A.S. EDOR was conceived by M.S. Data collection and analysis were performed by M.S. and M.V. The MATLAB code was written by M.S. and S.P. Samples were designed by J.E. and prepared by I.M. The manuscript was prepared by M.S., S.P. and M.J.D.

COMPETING INTERESTS

The authors declare no conict of interest.

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